
rennen
to run
To move very quickly on foot; to run fast.
Die Kinder rennen um die Wette zum Spielplatz.
The children run to the playground in a race.
to run
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to run
To move very quickly on foot; to run fast.
Die Kinder rennen um die Wette zum Spielplatz.
The children run to the playground in a race.

to rush
Colloquial for hurrying or rushing in order to get somewhere.
Ich muss jetzt zur Post rennen, sonst macht sie zu.
I have to rush to the post office now, otherwise it will close.

to run into a wall
To encounter insurmountable resistance or fail in an undertaking.
Mit diesem Vorschlag wirst du bei der Geschäftsführung gegen eine Wand rennen.
With this proposal, you will run into a wall with management.
As a verb of fast movement, 'rennen' (to run) always forms the perfect tense with the auxiliary verb 'sein' (to be). A common mistake is using 'haben' (to have).
Ich bin zum Bahnhof gerannt, um den Zug noch zu erwischen.
I ran to the station to still catch the train.
To emphasize the high speed, 'rennen' (to run) is often combined with certain expressions. Examples are 'um sein Leben rennen' (to run for one's life), 'um die Wette rennen' (to race), or 'so schnell man kann rennen' (to run as fast as one can).
Als der Hund bellte, ist das Kind schnell weggerannt.
When the dog barked, the child quickly ran away.
When 'rennen' (to rush) is used in the sense of 'sich beeilen' (to hurry), it is typical of colloquial language. In more formal contexts, you would use other verbs.
Ich muss noch schnell zur Bank rennen, bevor sie schließt.
I still have to quickly rush to the bank before it closes.
The expression 'gegen eine Wand rennen' (to run into a wall) is a fixed idiom. It means that you meet insurmountable resistance with a plan or idea and have no success.
Mit seiner Idee ist er bei seinem Chef leider gegen eine Wand gerannt.
Unfortunately, he ran into a wall with his idea when he brought it to his boss.
to run
Laufen and rennen both describe moving quickly on foot. Laufen is the more general term and does not indicate a particularly fast pace; rennen emphasizes very high speed. Use laufen at a normal running pace and rennen for a sprint.

Paul rennt so schnell wie möglich zum Ziel.
Paul runs toward the finish as fast as possible.
Paul läuft in gleichmäßigem Tempo zum Ziel.
Paul runs toward the finish at a steady pace.